Midpoint of a Straight Line Segment

Date: 5/7/96 at 16:18:16
From: Greg Williams
Subject: What is the midpoint?
Geometry: What is the midpoint of this: (-3,4) (5,-4)?
Use the distance formula.
Thanks a bunch.
Greg Williams of Tallwood High School in Virginia Beach, VA.

Date: 8/27/96 at 15:4:15
From: Doctor Mike
Subject: Re: What is the midpoint?
Hello Mr. Williams,
The midpoint of a straight line segment can always be found by
averaging the x-coordinates and averaging the y-coordinates. For
your example you get (1,0). The distance formula will give you
sqrt(32) for the distance from each end to (1,0). It will also give
you 2*sqrt(32) for the distance between the original 2 points. That
pretty much proves the answer.
In general, you can do the same thing with (A,B) , (X,Y) and
/ A+X B+Y \
( ----- , ----- )
\ 2 2 /
Hint: you'll have to keep things like (A-X)^2 = (X-A)^2 in mind.
I hope this helps.
-Doctor Mike, The Math Forum
Check out our web site! http://mathforum.org/dr.math/